1. Exam Review Chapters 7-13

2. Q1. Expand: (2 - 3y) 4

3. A1. 16 – 96y + 216y 2 - 216y 3 + 81y 4

4. Q2. Find the coefficient of a 6 in (5 – 3a) 10. ix x)

5. A2. 95,681,250

6. Q3. Find the 8 th term in the expansion of (2x – 3) 15.

7. A3. -3,602,776,320x 8

8. Q4. State the Law of Sines.

9. A4. sinα = sinβ = sin γ a b c

10. Q5. State the Law of Cosines.

11. A5. a² = b² + c² - 2bccosα

12. Q6. State the Pythagorean Identity.

13. A6. cos²θ + sin²θ = 1

14. Q7. A vector is a quantity with ? and ?.

15. A7. magnitude and direction

16. Q8. A vector with a magnitude of one is called a ?.

17. A8. unit vector

18. Q9. A vector whose initial point is at the origin is called a ?.

19. A9. position vector

20. Q10. If v = ai + bj, then a and b are called the ?.

21. A10. components

22. Q11. The set of all points equidistant from a point and a line is called a(n) ?.

23. A11. parabola

24. Q12. The set of all points such that the sum of the distances from two fixed points is a constant is called a(n) ?.

25. A12. ellipse

26. Q13. The set of all points such that the difference of the distances from two fixed points is a constant is called a(n) ?.

27. A13. hyperbola

28. Q14. The line associated with a parabola is called the ?.

29. A14. directrix

30. Q15. The two fixed points of an ellipse or hyperbola are called ?.

31. A15. foci

32. Q16. Which conic has transverse and conjugate axes?

33. A16. hyperbola

34. Q17. What equation will help you find the foci for a hyperbola?

35. A17. b² = c² - a²

36. Q18. Identify the conic:

37. A18. hyperbola

38. Q19. A rectangular array of numbers is called a(n) ?

39. A19. matrix

40. Q20. A triangular display of binomial coefficients is called ?

41. A20. Pascal’s Triangle

42. Q21. What are the dimensions of the following matrix?

43. A21. 3 x 1

44. Q22. Write I 3.

45. A22.

46. Q23. A sequence is a function whose ? is the set of positive integers.

47. A23. domain

48. Q24. A sequence whose difference between successive terms is a constant is ?.

49. A24. arithmetic

50. Q25. A sequence whose ratio between successive terms is a constant is ?.

51. A25. geometric

52. Q26. Evaluate:

53. A26. 55

54. Q27. A vector with a magnitude of zero is called a ?.

55. A27. zero vector

56. Q28. Evaluate: a.) p(0) b.) lim p(s) x→0

57. A28. a.) 0 b.) DNE

58. Q29. Evaluate: a.) G(2) b.) lim G(x) x→2

59. A29. a.) 3 b.) 1

60. Q30. Name another polar coordinate for (-2, -π/3)

61. A30. (-2, 5π/3) (2, 2π/3) (2, -4π/3)

62. Q31. Convert to polar coordinates: (-4, 0)

63. A31. (4, π) (4, 180˚)

64. Q32. Convert to rectangular coordinates: (-2, 5π/6)

65. A32. (√3, -1)

66. Q33. Write the rectangular form of the equation: r = 4sinθ

67. A33. x² + (y-2)² = 4

68. Q34. How many petals does r = 3cos5θ?

69. A34. 5

70. Q35. In which quadrant does -1 – 5i fall?

71. A35. III quadrant

72. Q36. Identify the graph: r = 4 – 5cosθ

73. A36. limaçon with inner loop

74. Q37. In which quadrant does the point with polar coordinates of (-3,2π/3) fall?

75. A38. IV quadrant

76. Q39. Simplify: cos 2 62˚ + sin 2 62˚

77. A39. 1

78. Q40. What is the length of the hypotenuse in the right triangle below? 43˚ 7

79. A40. 10.26

80. Q41. Find a: 14 38˚ 8 a

81. A41. no such triangle

82. Q42. If v · w = 0, then the two vectors v and w are ?.

83. A42. orthogonal

84. Q43. If v x u = 2i + j – 3k, then u x v =

85. A43. -2i – j + 3k

86. Q44. The following is the standard equation for which conic?

87. A44. hyperbola

88. Q45. Solve: 6x – 4y = 20 4x + y = 6

89. A45. (2, -2)

90. Q46. Solve: x² – y = 4 2x + y = -1

91. A46. (-3, 5) (1, -3)

92. Q47. Solve: x + y + z = 3 x - z = 1 y – z = -4

93. A47. (3, -2, 2)

94. Q48. Solve: x – √5y = 2.7 3.4x + 2y = 6.1

95. A48. (1.983, -.321)

96. Q49. Evaluate:

97. A49. 0

98. Q50. Evaluate:

99. A50. -2.56

100. Q51. Evaluate:

101. A51. 4

102. Q52. Evaluate:

103. A52. 3